The auxiliary region method: A hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems

Reaction-diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with varying degrees of accuracy and computational efficiency. When representing genuinely multiscale phenomena, fine-scale models can be prohibitively expensive, whereas coarser models, although cheaper, often lack sufficient detail to accurately represent the phenomenon at hand. Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy. In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE and Brownian-based representations of reaction-diffusion systems. Numerical PDE solutions on one side of an interface are coupled to Brownian-based dynamics on the other side using compartment-based "auxiliary regions". We demonstrate that the hybrid method is able to simulate reaction-diffusion dynamics for a number of different test problems with high accuracy. Further, we undertake error analysis on the ARM which demonstrates that it is robust to changes in the free parameters in the model, where previous coupling algorithms are not. In particular, we envisage that the method will be applicable for a wide range of spatial multi-scales problems including, filopodial dynamics, intracellular signalling, embryogenesis and travelling wave phenomena.Comment: 29 pages, 14 figures, 2 table

Categorical Data

A very brief survey of regression for categorical data. Categorical outcome (or discrete outcome or qualitative response) regression models are models for a discrete dependent variable recording in which of two or more categories an outcome of interest lies. For binary data (two categories) probit and logit models or semiparametric methods are used. For multinomial data (more than two categories) that are unordered, common models are multinomial and conditional logit, nested logit, multinomial probit, and random parameters logit. The last two models are estimated using simulation or Bayesian methods. For ordered data, standard multinomial models are ordered logit and probit, or count models are used if ordered discrete data are actually a count.binary data, multinomial, logit, probit, count data

The Aging Population and the Size of the Welfare State: Is There a Puzzle?

Razin, Sadka, and Swagel (2002) unveil a puzzling fact: the welfare state appears to be shrinking even as the dependency ratio rises. While they formulate an elegant political economy model to explain the coexistence of an aging population and declining transfers, the resolution of the puzzle turns out to be much simpler. Labor tax rates and per capita transfers are negatively correlated with the dependency ratio in advanced economies only because this measure includes children as well as retirees. Both labor tax rates and per capita transfers in advanced economies are, in fact, historically positively correlated with the ratio of retirees to the working-age population and negatively correlated with the ratio of children to the working-age population. Increasing the number of retirees shifts preferences toward higher taxes and transfers by increasing the fraction of the population that receives transfers. In contrast, workers with more children prefer to spend more of their lifetime income while raising dependents, so they prefer smaller public pension systems. These results suggest that fiscal leakage from workers to retirees is not required to explain the broad trends in the transfer policies of advanced economies.dependency ratio, welfare state

The Size and Composition of Government Expenditure

This paper tests several leading hypotheses on determinants of government expenditure. The purpose is to avoid omitted variables bias by testing the prominent theories in a comprehensive specification, to identify persistent puzzles for the current set of theories, and to explore those puzzles in greater depth by looking at the composition of government expenditure and the level of government at which it takes place as well as its magnitude. Using Global Financial Statistics data from the IMF covering over 100 countries from 1970-2000, I look at cross-sectional and inter-temporal variation in government expenditure and both individual categories of expenditure (such as defense, education, health care) and different levels of government (central, state, and local). Among other results, I find a new explanation for Wagner's Law, widespread evidence that preference heterogeneity leads to decentralization rather than outright decreases in expenditures, that a great deal of the expenditure associated with increased trade openness is not in categories that explicitly insure for risk, and evidence that both political access and income inequality affect the extent of social insurance.government expenditure, Wagner's Law

The early evolution of the solar system

The problems of relating collapse conditions in an interstellar cloud to a model of the primitive solar nebula are discussed. In such a nebula there is a radial force balance between gravity, the pressure gradient, and centrifugal forces due to the rotation. Approximate values are given for the combinations of temperature and density throughout the nebula, from a maximum of about 2000 K near the center to less than 200 K in the outer portion. These conditions are based upon the compression adiabats in the terminal stages of the collapse of an interstellar cloud. One general conclusion, of great importance for accumulation of bodies within the solar system, is that interstellar grains should not be completely evaporated at distances in the nebula beyond about one or more astronomical units

The tasks and roles of social workers: a focused overview of research evidence

Options for Excellence is a joint DfES and DH-funded review of the social care workforce. Four task groups have been set up, each dealing with different aspects of social care. Task Group 3 is considering the roles and tasks of social workers. In order to inform the work of this group, the Thomas Coram Research Unit was asked to provide an overview of relevant research and data in three main areas: the effective deployment of social worker time and tasks, improving cross-professional working, and attitudes to take-up of post-qualifying qualifications